On some practical issues concerning the implementation of Cahn–Hilliard–Navier–Stokes type models

Abstract

Suspensions, solutions and colloids are physical systems that can be generally denoted as “multicomponent systems” or “mixtures”. Physical systems of this type are frequently met in many industrial applications which rises the need for numerical simulations of the behaviour of such complex systems.
A particular practical example of such system is glass/tin/nitrogen system that must be studied in modelling of the float glass process (Pilkington process) that partly motivated this research. The aim of this paper is to discuss the numerical challenges along with some practical issues concerning the implementation of a chosen Cahn–Hilliard–Navier–Stokes type model that showed up to be particularly suitable for the description of three-component systems. The discretization of the system of governing partial differential equations is based on the finite element method using the FEniCS Project. Numerical experiments carried out in two and three spatial dimensions verify our straightforward implementation that uses parallel direct sparse solvers to resolve the intermediate linear systems of algebraic equations. Possible improvements of the current implementation are briefly outlined within the paper.

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The authors acknowledge the support of Project LL1202 in the programme ERC-CZ funded by the Ministry of Education, Youth and Sports of the Czech Republic. This work was supported by IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070), funded by the European Regional Development Fund and the national budget of the Czech Republic via the Research and Development for Innovations Operational Programme, as well as Czech Ministry of Education, Youth and Sports via the project Large Research, Development and Innovations Infrastructures (LM2011033).